Full waveform inversion using combined shot data and no scratch disk

ABSTRACT

A system, method and computer program product for seismic imaging implements a seismic modeling algorithm utilizing Forward Wave Inversion technique for revising Reverse Time Migration models used for sub-surface modeling. The technique requires large communication bandwidth and low latency to convert a parallel problem into one solved using massive domain partitioning. The partitioning of a velocity model into processing blocks allows each sub-problem to fit in a local cache, increasing locality and bandwidth and reducing latency. The RTM seismic data processing utilizes data that includes combined shot data, i.e., shot data selected from amongst a plurality of shots that are combined at like spatial points of the volume. An iterative approach is applied such that the correction term RTM generates at each iteration in the iterative approach is used for refining the model, and the updated model is used for generating a further refined RTM model.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §119(e) of U.S. Provisional Patent Application Ser. Nos. 61/495,886, filed Jun. 10, 2011, the disclosure of which is hereby incorporated by reference in its entirety.

This application relates to commonly-owned, co-pending U.S. Patent Application Ser. Nos. 61/495,892, 61/495,876, and 61/495,880, the whole contents and disclosure of each of which is incorporated by reference as if fully set forth herein.

The present invention relates generally to seismic imaging systems and processes, and particularly, to improvements related to systems and processes for Full Waveform Inversion (FWI) seismic modeling.

BACKGROUND

Seismic imaging is the process of converting acoustic measurements of the Earth into images of the Earth's interior, much like ultrasound for medical imaging. It is widely used in oil and gas exploration and production to identify regions that are likely to contain hydrocarbon reservoirs and to help characterize known reservoirs to maximize production. These methods have become critical to the energy industry as known reserves are used up and new reserves become increasingly difficult (and expensive) to find and are increasingly in technically challenging areas, like the deep sea. For the past several decades, the energy industry has tried to balance the need to image quickly and the need to image accurately. The need for accuracy is driven by the high cost of drilling a “dry” well due to poor imaging (a deep sea well can cost over $100 million) and the need for quick imaging is driven by the cost of not finding new reserves (i.e., bankruptcy). To minimize these costs, the industry relies on supercomputing clusters and regularly increases compute power, enabling both faster imaging on existing algorithms and the practical implementation of more accurate imaging. Thus, the development of fast, efficient methods for imaging is of high importance to the industry.

Seismic imaging data varies widely depending on how and where the data is collected (e.g., on land, at sea, at the ocean surface, at the ocean floor, below ground, electromagnetically, etc). One data collection method in particular implements a towed hydrophone receiver arrays for ocean seismic data collection. The basic idea is shown in FIG. 1 depicting a ship 200 shown towing a 2D array 212 of hydrophones spaced about every 25 m on 1 to 16 trailed streamers. Every 15 or so seconds, an air cannon is fired into the water creating an acoustic wave, e.g., a shot 211 that propagates through the water and into the Earth. Reflections from various surface and subsurface boundaries cause echoes that reflect back and are recorded by each hydrophone in the array 212. The recording of a single hydrophone in time as a trace and the collection of traces for a single firing of the air cannon is called a common shot gather, or shot. As the ship 200 moves, a large set of spatially overlapping shots is recorded. Depending on the size of the survey region to be imaged, this data collection can take a month or more and is designed to get the maximal coverage of the area to be imaged. The receiver data R(x, y, z, t) collected for potentially hundreds of thousands of shots is the result of some source data S(x, y, z, t) at a particular location.

A sample of artificial shot data is shown in FIG. 2 showing a sample shot data 215 for a 1D array of hydrophones showing time on the Y-axis and spatial offset on the X-axis. The direct source signal propagates out linearly in time (from the center of the array) and appears as straight lines 216. The recorded reflections appear as curved lines 218.

Two critical requirements drive production seismic imaging: The need for improved imaging to accurately locate and characterize elusive oil and gas reservoirs; and the need for timely subsurface imaging. Drilling too soon risks expensive dry wells while drilling too late risks delaying the time to oil. To minimize these risks, the industry regularly increases the power of its supercomputing clusters, enabling both faster imaging on existing algorithms and the practical implementation of more accurate imaging. However, raw supercomputing power is not enough. It is equally important—if not more so—to implement algorithms efficiently based on a detailed knowledge of the hardware.

The Reverse Time Migration (RTM) algorithm (see, e.g., Zhou, H., Fossum, G., Todd, R. and Perrone, M. 2010 Practical VTI RTM in Proceedings of 72nd EAGE Conference) is widely used in the industry because of its superior imaging accuracy for difficult subsurface structures like salt domes which are poorly imaged by other algorithms but which are very effective at trapping oil and gas. Several variants of RTM exist with differing degrees of approximation to reality, all of which use single-precision arithmetic.

Historically seismic imaging has processed shot gathers individually on a single compute node so that they could be processing in parallel. This approach has many benefits; but for algorithms like RTM, as computational power increases, data I/O becomes the single largest performance bottleneck, particularly when the model is large.

The RTM algorithm arises from the observation that pressure waves should be correlated at reflection boundaries; so RTM proceeds by correlating two pressure waves (called the forward and backward waves) to find those boundaries. To generate the waves for correlation, RTM simulates wave propagation using the wave equation below for a wave U(x,y,z,t) with a source term S(x,y,z,t):

$\begin{matrix} {{\frac{1}{c^{2}}\frac{\partial^{2}U}{\partial t^{2}}} = \left. {\frac{\partial^{2}U}{\partial x^{2\;}} + \frac{\partial^{2}U}{\partial y^{2}} + \frac{\partial^{2}U}{\partial z^{2}} + S} \right|} & \left. 1 \right) \end{matrix}$

The forward wave is the wave generated from the air cannon firing and propagating forward in time using a “velocity model” represented by C(x,y,z), which specifies the wave velocity at each point in space and represents the various material properties and boundaries of the volume being imaged. The air cannon firing is treated as a wavelet impulse localized in time and space. The backward wave is generated by using the shot data recorded by the hydrophone array as the source term for the wave equation and propagating that backward in time. These two waves are then multiplied point-wise at each time step to generate an image, using the following “imaging condition”: I(x,y,z)=Σ_(t) U _(Forward)(x,y,z,t)U _(Backward)(x,y,z,t)  2)

This process is repeated for all shots in the seismic survey and the images generated are summed to create a final image of the reflecting boundaries, which represent the subsurface structure. It is important to note that the time summation in the imaging condition implies that the first time step of the forward wave needs to be correlated with the last time step of the backward wave. This constraint is typically handled in one of two ways: either the forward wave is saved to disk (called a “snapshot”) every time step or every several time steps and read in for imaging when the backward wave is computed, or the forward propagation is run twice—once forward in time and once in reverse time using boundary data saved from the forward pass to recreate the forward pass in reverse—and then imaging proceeds with the backward wave and the reverse forward wave.

The first method requires significant disk storage and can be bottlenecked on disk I/O, while the second requires 50% more computation and additional memory space to save the boundary data. Following standard practice in the industry as described in Zhou, et al. 2010, the wave propagation of Equation (1) is simulated using the finite difference approximation in formula (3) where there is selected the coefficients to implement 2^(nd) order accuracy in time and 8^(th) order accuracy in space. These coefficients are scaled to satisfy the CFL condition (Courant Friedrichs Lewy http://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs % E2%80%93Lewy_condition. This approach gives rise to a stencil shown in FIG. 3 which depicts a 25-Point spatial stencil 220 with 8th order accuracy shown in isolation on the left and the stencil 222 as it moves along the stride-1 dimension of the model.

$\begin{matrix} {U_{i,j,k,{t + 1}} = {{2U_{i,j,k,t}} - U_{i,j,k,{t - 1}} + {c_{i,j,k}^{2}{\sum\limits_{n = {- 4}}^{n = 4}\left( {{A_{xn}U_{{i + n},j,k,t}} + {A_{yn}U_{i,{j + n},k,t}} + {A_{zn}U_{i,j,{k + n},i}}} \right)}}}} & \left. 3 \right) \end{matrix}$

Where the A's are the stencil coefficients and can be determined using known methods and subscripts i, j, k are the indices of a pointing a 3D (or 1D or 2D) velocity model. In practice, the size of production RTM models varies widely, but the universal desire is to grow models larger to get more resolution and to run the models longer to enable deeper imaging since echoes take longer to reflect from deeper structures.

Typically, velocity models for individual shots are 512³ to 1024³ elements or larger and the number of time steps can be 10,000 or more in both the forward and backward propagation phases. Seismic imaging is typically computed using single precision arithmetic.

Industrial implementations of RTM are embarrassingly parallel. They typically run individual shots on one to two nodes of a compute cluster and run many shots in parallel, e.g., one shot per slave node, as shown in FIG. 4. These clusters have minimal network connectivity because it is not needed: the individual shots run independently and asynchronously. A simple work queue is used to manage runs and if a run for a shot fails, it is simply re-run, as it doesn't impact any of the other runs. A master process running at node 230 manages the work queue and to merge the partial images that are generated from each shot. Additionally, other image processing (not shown) might be included in this process.

As shown in FIG. 4, a velocity model V( ) 225 is conceptually depicted with each sub-block 28 representing a sub-set of the model data corresponding to a single shot. For calculating an image, the entire model is not needed, e.g., a sub-set of the model is used for a selected shot. A master processing node 30 in communication with a memory storage device, e.g., database 235, is programmed to allocate a RTM compute cluster 240 including a plurality of slave nodes 245, each node 245 having a corresponding memory storage device 250. Each slave node 245 is in communication with the master node 230 and is configured to obtain and process the single shot data 228 a. When a (forward or reverse) pressure wave and resulting image is calculated at a respective node, it is stored to the main memory storage disk 250. Memory storage devices 250 that store intermediate results data in calculating the forward or reverse pressure wave which values are used to calculate resulting image are referred to as “Scratch” disks. RTM compute clusters 40 have significant per-node scratch disk requirements for saving snapshot data, which for a 1024³ model and 10,000 time steps would require 40 TB of snapshot storage—per shot. In practice, snapshot sub-sampling is used to reduce both disk requirements and disk I/O bottlenecks; however sub-sampling results in image degradation and must be balanced with performance. Compression can be used to trade computation for disk I/O, but if lossy, compression can also degrade image quality.

The velocity model 225 is the representation of the velocity of the wave traveling at an x, y, z coordinate in the sub-surface of the earth, and, for purposes of description, is referred to as V². As velocity model 225 is not known in the RTM process, an imaging condition enables the snapshot of the wave at a particular point in time after calculating forward wave and backward waves. For every value of t there is produced an image from an average of many shots. When averaging many shots, the image at a coordinate at a time t, i.e., I(x,y,z) is obtained via the imaging condition according to: I(x,y,z)=Σ_(t) P _(S)(x,y,z,t)P _(R)(x,y,z,t)  4) where P_(S)(x, y, z, t) is the reflected forward power pressure wave at a coordinate and P_(R)(x,y,z,t) is the reverse power pressure wave at an x, y, z coordinate at a time t. In a high-level aspect the forward motion calculation, the velocity model v(x,y,z) is loaded, the pressure wave is loaded at time t and the previous pressure wave at time t−1, i.e., P(x,y,z,t−1); and the next pressure wave P(x,y,z,t+1) is computed (bootstrap) and is stored. This process is performed at each iteration (time step t). The wave field is a 3-D object and is very large (e.g., on the order of 1024³ elements). Thus, for example, at four bytes of data for each calculation, this may amount to 4 GBytes of data for 1 time step of the algorithm for a single shot) and there may be thousands of time steps amounting to over 24 TB of data for a single shot which, when sent out to disk, is time consuming. Thus in practice, in an effort to reduce the data, the data is not stored or calculated at every time step, i.e., the calculated P_(S)(x,y,z,t) is either stored or loaded to disk every N^(th) iteration.

Standard finite difference RTM is implemented as follows: (1) Compute the (forward) wave equation with shot source terms, saving “snapshots” of the entire wave field to disk every Nth time step; and (2) Compute the (reverse) wave equation with receiver source terms, reading in corresponding forward wave field snapshots and computing an imaging condition to incrementally generate an image. This process is repeated for each shot and the resulting images are merged to generate a final image. RTM has several variants depending on the complexity of the wave equation used (e.g., isotropic, VTI (Vertical Transverse Isotropy), TTI, (Tilted Transverse Isotropy). Analysis of RTM codes suggest that typically computation is not the performance bottleneck for these algorithms but rather the movement of data, particularly on and off disk, is the primary performance bottleneck. So it is essential that close attention be paid to the movement of data in order to develop fast RTM applications.

As FLOPS per processor increase, the prior art parallel implementations become disk I/O bound. It is possible to improve performance by partitioning single shot gathers over multiple nodes; however, such implementations typically use only a handful of nodes. Furthermore, in the prior art implementations, the inter-processor or node communications are severely limited by their bandwidth and thus results in large latency.

Full Waveform Inversion (FWI) has gained more and more attention for its application in pre-stack seismic model building and validating. Pre-stack plane-wave FWI is based on minimizing a cost function that measures the difference between the calculated and gathered data. In the prior art, forward propagated source wave-field derived from higher-order, staggered-grid, finite-difference approximation of the acoustic-wave equation is calculated and is then compared with gathered data. Their difference is checked to determine if the model is close to the actual data. If the model is not valid, then the residue between the calculated and gathered data is used to generate the backward wave-field in reverse-time propagation. The two wave-fields are cross-correlated and summed over all the time instances and shots to generate the correction term for the model updating and the process is repeated until the model converges.

That is, in current FWI solutions, such as in “3D prestack plane-wave, full-waveform inversion”, (D. Vigh and E. W. Starr, Geophysics, Vol. 73, No. 5, 2008) and U.S. Pat. No. 7,373,252 B2, all the intermediate data (both forward and backward wave-fields) need to be stored. Because the amount of the data is in the tens of terabytes and the computing systems do not have storage to hold the data, it has to be put in the external disks and read back when it is used. Similarly, in the prior art FWI solutions, all the shot data, also in the amount of terabytes, need to be read into the memory from the external disk for every iteration. Because the disk input and output operations have large latency, the FWI processes have become disk I/O bound in the prior art solutions; Consequently FWI solutions in the prior art are very time consuming. Therefore, it is very desirable to develop new FWI computing apparatus and methods to significantly improve the time performance over the prior art solutions.

SUMMARY

A system, method and computer program product for seismic imaging implements a seismic modeling algorithm utilizing Forward Wave Inversion technique for revising Reverse Time Migration models used for sub-surface modeling.

Using massive domain partitioning, wherein a velocity model is partitioned into processing blocks, allows each sub-problem to fit in a local cache, increasing locality and bandwidth and reducing latency.

The RTM seismic data processing utilizes data that includes single shot data or combined shot data, i.e., shot data selected from amongst a plurality of shots that are combined at like spatial points of the volume. An iterative approach is applied such that the correction term RTM generates at each iteration in the iterative approach is used for refining the model, and the updated model is used for generating a further refined RTM model.

The method includes running multiple shots simultaneously by combining them together, that is, the source data (wavelet) will be combined together for each of the shots, and the receiver data for multiple shots are combined together.

For example, shots may be randomly sampled (e.g., 1000 shots of 100,000 shots), the selection process includes the selecting a subset of all shot data and combining them in a combining step.

It is desired to provide a system and method that includes replacing a parallel implementation of an RTM imaging problem with a synchronized, communication intense, massive domain-partitioned approach.

In one aspect, there is provided an RTM implementation that extends domain partitioning over thousands of nodes on a distributed processor/memory supercomputer and results in increased performance improvements.

Thus, according to one aspect, there is provided a system, method and computer program product for creating a seismic model of sub-surface formations in a defined 2D or 3D volume of a geological structure. The method comprises: partitioning a velocity model domain representing a subsurface structure of the earth in the defined volume into a plurality of blocks, each block having an associated processing task for processing wave data associated with a shot; receiving, at local storage devices, data representing measurement each wave produced by a shot of a sequence of plural shots; and assigning each partitioned domain block to one or more processing nodes of a distributed processing highly parallel computer device having a plurality of processing nodes interconnected through one or more communication networks; computing, in parallel, using the associated processing tasks operating on the receiver data associated with a shot at each the processing node, contributions of forward wave propagation data and reverse wave propagation data at that node, the reverse wave propagation data computed using a residual data from forward wave propagation data computing; and, using the computed forward wave propagation data and reverse wave propagation data contributions to compute a correction term from which the seismic model is updated.

In a further aspect, there is provided a computer-implemented system and method for creating a seismic model of sub-surface formations in a defined 2D or 3D volume of a geological structure. The method comprises: partitioning a velocity model domain representing a subsurface structure of the earth in the defined volume into a plurality of blocks, each block having an associated processing task for processing wave data associated with a shot; receiving, at local storage devices, data representing measurement each wave produced by a shot of a sequence of plural shots; assigning each partitioned domain block to one or more processing nodes of a distributed processing highly parallel computer device having a plurality of processing nodes interconnected through one or more communication networks; combining, at a respective partitioned node, receiver data of two or more shots to form a metashot, the associated processing tasks operating on the formed metadata at each the processing node; computing, in parallel, using the associated processing tasks operating on the receiver data associated with a shot at each the processing node, contributions of forward wave propagation data and reverse wave propagation data at that node, the reverse wave propagation data computed using a residual data from forward wave propagation data computing; and, using the computed forward wave propagation data and reverse wave propagation data contributions to compute a correction term from which the seismic model is updated.

Further to this aspect, the computer-implemented method further comprises: configuring each the node for pipelined processing wherein the forward or reverse wave propagation components are computed/stored at the processing node for current metashot data while new data for the next metashot is loaded into a local memory at each node.

In a further aspect, there is provided a system for creating a seismic model of sub-surface formations in a defined volume of a geological structure. The system comprises: an array of receiver devices at or within said defined volume for recording data representing measurements of each wave produced by a shot of a sequence of plural shots; a distributed processing highly parallel computer device having a plurality of processing nodes interconnected through one or more networks, each node having a respective processor device and a local memory storage device associated with the respective processor device, wherein one or more said processing nodes is assigned a processing block representing one partition of a partitioned velocity model domain representing geophysical wavefield propagation characteristics of a sub-surface structure of the earth in said defined volume, each processing block having an associated processing task for processing wave data associated with a shot; wherein a processor device at each node is configured to perform, in parallel, a method comprising: combining, at a respective partitioned node, receiver data of two or more shots to form a metashot, said associated processing tasks operating on said formed metadata at each said processing node; computing, in parallel, using said associated processing tasks operating on said receiver data associated with a shot at each said processing node, contributions of forward wave propagation data and reverse wave propagation data at that node, said reverse wave propagation data computed using a residual data from forward wave propagation data computing; and, using said computed forward wave propagation data and reverse wave propagation data contributions to compute a correction term from which the seismic model is updated.

A computer program product is provided for performing operations. The computer program product includes a storage medium readable by a processing circuit and storing instructions run by the processing circuit for running a method. The methods are the same as listed above.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects, features and advantages of the present invention will become apparent to one skilled in the art, in view of the following detailed description taken in combination with the attached drawings, in which:

FIG. 1 depicts one RTM seismic data collection method implementing a towed hydrophone receiver arrays for ocean seismic data collection;

FIG. 2 depicts an example sample shot data for a 1D array of hydrophones showing time on the Y-axis and spatial offset on the X-axis;

FIG. 3 depicts an 25-point spatial stencil with 8th order accuracy shown in isolation on the left and as it moves along the stride-1 dimension of the model;

FIG. 4 shows parallel implementation of RTM that typically run individual shots on a node of a compute cluster and run many shots in parallel wherein the node implements scratch disk storage;

FIG. 5 depicts a method for calculating the RTM imaging condition according to a one embodiment;

FIG. 6 depicts the velocity model being partitioned into indivisible objects that each are individually assigned to a respective slave node for handling memory storage operations locally in one embodiment;

FIG. 6A depicts conceptually the stencil computations requiring neighboring node data communications in one embodiment;

FIG. 7A depicts a first embodiment of the model for calculating the imaging condition using massively parallel computing system with local node memory storage according to one embodiment;

FIG. 7B depicts a second embodiment of the model for calculating the imaging condition using massively parallel computing system with local node memory storage according to one embodiment;

FIG. 8 depicts a node ASIC 10 for a massively parallel supercomputer such as may be implemented in the Blue Gene/P computing system for RTM seismic data processing;

FIG. 9 depicts each compute node being connected to six (6) neighboring nodes via 6 bi-directional torus links as depicted in the three-dimensional torus sub-cube portion implemented by the Blue Gene/P computing system for RTM seismic data processing;

FIG. 10 shows the method for FWI Seismic Image processing according to one embodiment.

DETAILED DESCRIPTION

A system and method is described for operation in a distributed-memory supercomputer using a network as a high performance data communication mechanism for partitioning each shot gathered among a subset of the computing nodes and performing RTM seismic imaging in a collaboration fashion.

While several variants of RTM seismic imaging exist with differing degrees of approximation to reality, in one embodiment, for purposes of discussion, it is assumed that there is implemented isotropic, acoustic RTM which assumes the wave velocity is independent of wave direction and that no energy is absorbed by the medium.

In one example embodiment, the present system and method operates in a massively parallel computing system such as the Blue Gene® (trademark of International Business Machines Corp., Armonk N.Y.) computing system. The RTM implementation extends domain partitioning over thousands of nodes on a Blue Gene® computing system.

The method implemented in the Blue Gene System® uses its aggregate memory as a high performance data fabric for handling intermediate data in Reverse Time Migration (RTM) seismic imaging process thereby alleviating the disk storage requirements in conventional RTM processing and thus reducing the cost of the system.

The total aggregate memory of the Blue Green® computing system is distributed in the style of a multi-computer. With each compute node supporting up to 4 GB physical memory, a rack of the Blue Gene® system can have up to 4 TB aggregate memory.

The Blue Gene® system makes use of its torus network configuration as a high performance data communication mechanism for partitioning each shot gathered among a subset of the Blue Gene® nodes and performing RTM seismic imaging in a collaboration fashion. Processing performance is improved by alleviating disk I/O operations during the course of the RTM processing.

Referring to FIG. 6 there is depicted the velocity model 125 that is partitioned into indivisible objects 128 that each individually is assigned to a respective slave node 145 in the Blue Gene® system. Any shot data within that object is thus assigned to and processed by that slave node. In one embodiment, the partitioning of the velocity model 125 is performed according to a uniform spatial partitioning scheme, in which each dimension of the model is divided into equal- or approximately equal-sized groups of points creating the blocked structure shown in FIG. 6A, or, a non-uniform spatial partitioning scheme. Null padding of dimensions can be used to assure that each block is exactly the same size. In another embodiment, the partition can be done non-uniformly so as to balance the amount of work required for each block. The configurability of the partitioning may be motivated by a minimizing the run time. In such an embodiment, the block would not be necessarily be the same size. The specific choice of non-linear partition can be driven by profiling of particular code implementations. Each implementation includes boundary handling data including data representing the boundary conditions of the model 125, e.g., at edge 126, for example.

Rather than processing each shot data in parallel, a slave node 145 receives data 128 a from multiple shots, i.e., shots (single shot or trace data) being partitioned among the slave nodes 145 of a cluster. Via partitioning, the velocity model (e.g., amounting to over 24 TB of data memory required for processing a single shot with a model order of 1024³ which may amount to 4 GBytes of data for 1 time step of the RTM imaging algorithm for a single shot per slave node and there may be thousands of time steps)) is thus divided, e.g., amongst “n” slave nodes 145; therefore, for example, for n=1000 slave nodes, with partitioning, each slave node would need only enough memory to process its assigned part of the velocity model (e.g., 4 MB of the model) with data requirements of only 24 GBytes per node. Thus, via partitioning, each slave node 145 has enough local memory to manage processing of the velocity model portion without having to store data in the scratch disk. That is, the entire model is kept in memory at each slave node, obviating the need for scratch disk, and the attendant disk-bandwidth bottleneck. In Blue Gene® supercomputer implementations the bandwidth to main memory on the computer governs (e.g., 10 MB/sec) such that one (1) rack of a Blue Gene® computer, can process data of a 512³ velocity model data in about 30 sec.

That is, as described in greater detail below, in one embodiment, there is performed domain partitioning for seismic imaging to improve the overall run-time performance of the seismic imaging system. In one embodiment, an example process of domain partitioning implemented by a computing device, for example, includes: 1) defining a domain (e.g., a cubic velocity model of size N³ elements) or some complex shape); 2) dividing that domain, using methods known to those skilled in the art, into two or more distinct or overlapping subsets; 3) processing each subset of the domain on a separate node of a supercomputer. For example, the processing may include a physical simulation like for seismic imaging or any other supercomputing calculation; 4) synchronizing the nodes so that all calculations have completed; 5) communicating information between nodes (sometimes to all nodes, sometimes to a fixed subset (like nearest neighbors) and sometimes to a dynamic subset that changes with each iteration—depending on the algorithm that is being run—e.g., RTM using nearest neighbors); and, 6) iterating over steps 1-5 as many times as is needed. Generally steps 1 and 2 are not repeated. It should be understood that alternative to a cubic velocity model of size N³ elements 1-Dimensional and 2-Dimensional versions may be used and follow the same algorithm.

FIG. 5 depicts a method 60 for calculating the RTM imaging condition in a massively parallel computing system according to a one embodiment. As mentioned, one implementation includes the Blue Gene® computing system. First, at 62, there is input to the nodes of the system a data set including the velocity model v(x,y,z) and associated model parameters (e.g., Isotropy, VTI, TTI) which are loaded to the respective local node memories. The parameters are run to configure the node for the RTM seismic imaging processing. For example, theses may include the code execution parameters, i.e., the model size (e.g., the size(s) of the model partitioning as determined by details of the hardware implentations—e.g., IBM Power7, BlueGene®, Intel Xeon Westmere Clusters, etc.), the iteration numbers, the snapshot frequency, etc. Further input as part of data set are the Shot Data (Source/Receiver Data); the source data being created by an air cannon or other noise source but is modeled at each node using a “wavelet” (a finite wave that can be represented in numerous ways, data represented as a mathematical function(s), or experimentally obtained and used subsequent) as known to those skilled in the art. There are many specific wavelets that can be used, e.g., a Ricker wavelet in one implementation (http://en.wikipedia.org/wiki/Mexican_hat_wavelet). The receiver data on the other hand is specifically recorded using the recording devices and it is these measurements that are used in the backward processing stage as input.

After configuring the domain partitioned nodes at 62, the source and receiver data are read from the storage device, whether external disk or locally. Depending upon the method, the embodiment considers that shot data may be incrementally obtained, e.g., according to a predetermined period or time interval. For example, shot data for that node may be obtained every k time steps.

Then, in a further step 64, the data is read as needed by the node. Data is read incrementally (i.e., the data is read as needed for the next shot while processing the current shot, not necessary as the whole), and is usually read at shot frequency or subshot frequency, e.g., every “k” time steps. Data is read from where the data is stored, e.g., local storage, and at 65, distributed for processing at each node, or a flash memory available at each node of the massively parallel system and/or may be stored in the node's associated scratch disk. In one aspect, all the data (e.g., including input data, receiver data, temporary calculations results, or intermediate result data) is stored to local memory storage (e.g., RAM, DD-RAM) at each compute node of the massively parallel system. However, in alternate embodiment, these types of data may be stored in a flash memory available at each node of the massively parallel system and/or may be stored in the node's associated scratch disk. It is understood that alternate embodiments contemplate various combinations of data storage as well, wherein data may be stored in each memory mode (local node memory, flash and/or disk).

At 66 there is performed partitioning of the model, i.e., the model space/data is partitioned into sub-spaces for the multiple nodes to process them in parallel. In an alternate embodiment, a hierarchical scheme may be implemented in which RTM processing progresses to obtain images at varying levels of detail, based on partition (model) sizes as will be described in greater detail herein below.

The next sequence of steps describes the processing at each node after the partitioning.

Continuing to 68, shot data is combined and the method includes merging the read shot data. This may include various steps that combine some or all shots from a seismic survey to form a metashot(s) in which an RTM algorithm may be used to process the resulting set of shots and/or metashots.

That is, the method and system combines multiple shots to form one or more “meta-shots”. These metashots are then processed by the RTM algorithm in the manner described. This dramatically reduces the use of scratch data during the RTM processing of a seismic survey.

The method includes running multiple shots simultaneously by adding them together, that is, the source data (wavelet) will be added together for each of the shots, and the receiver data for multiple shots are added together. For example, shots may be randomly sampled (e.g., 1000 shots of 100,000 shots), the selection process includes the selecting a subset of all shot data and combining them in the combining step.

In alternate embodiments, the combining may include: adding using only metashots (or adding a subset of the shot data at like time steps of shots or sub-set of shots at like spatial points of the volume wherein the subset of shot data is selected randomly or according to one or more rules); adding using unique shots for each metashot (a shot is never added to a metashot more than once); adding using a unique metashot for each shot (no shot used in more than one metashot); adding including a variable weighting factor when shots are combined into a metashot; adding using all shots combined into a single metashot; adding using combining shots as if they were all recorded at the same time; adding by combining shots with a time lag, wherein a weighting factor is used to reflect a phase (lag or lead) of the shots; adding by combining on a pre-specified grid for each time step; adding using a smoothing function to distribute the recorded data to the pre-specified grid. It is understood that a combination may include a linear superposition of the recorded waves or a nonlinear superposition, such as combination using phase-shift encoding.

Continuing to 70, a processing loop is entered in which there may be performed the RTM seismic imaging algorithm in accordance with one of two alternate embodiments 72A (forward-backward method), 72B (forward-forward-backward method) as will be described in greater detail herein below. Each of the RTM image data processing methods 72A, 72B seek to achieve an imaging condition of the sub-surface formations by calculating forward and reverse components of the propagating wave. Each of these steps, described herein with respect to FIGS. 7A, 7B preferably employ local memory storage for storing locally at the node memory, computed forward propagating wave components, however, can utilize local flash memory at the node and/or the attached scratch disk for the temporary storage.

For example, source data at the same location of the volume being modeled, from multiple shots (waves of different shots reaching the same place) the values of wavelets for each shot are added (combined) (values are added at single point of time and same spatial point). The receiver data for multiple shots is processed similarly where receiver data values of selected shots are combined. The shots used for the forward and backward wave processing may be randomly selected, in a non-limiting example.

Continuing to 74, as a result of forward and backward propagating wave processing implemented at 72A or 72B, the resulting partial images are merged to obtain the completed image. Continuing to 76, as the processing depicted in FIG. 5 may be performed over multiple shots, a determination is made as to whether there are any more shots to be processed. If there are more shots to be processed, then the process continues by returning to step 70 and repeating steps 72A or 72B and 74, 76, however, using additional or new shot data obtained at 75 as shown in FIG. 5. Otherwise, at step 76, if it is determined that there are no more shots (no more shot (or metashot) data) to be processed, the process concludes by outputting the final image at step 78.

As the method 60 shows, in one embodiment, the incremental loading of receiver data or trace data, e.g., a single shot at a time, or as merged shot data, permits pipelined operation. That is, from the loop programmed at each node from steps 70-76, while the forward or reverse wave propagation components are computed/stored at the processing node for the current trace data for a single shot (or combined metashot), new trace data for the next single shot (or combined metashot) is loaded into the memory for each node, or in a combination of memory modalities (flash and/or disk).

Referring back to step 70, in which a processing loop is entered in which there may be performed the RTM seismic imaging algorithm, FIG. 7A describes the processing according to alternate embodiment 72A, and FIG. 7B describes the processing according to alternate embodiment 72B

In FIG. 7A, there is calculated forward propagation pressure wave, P_(S)(x,y,z,t) at every N^(th) timestep. The reflected forward power pressure wave P_(S)(x,y,z,t) calculation at every N^(th) timestep is either stored and/or loaded to memory storage (alternately including storing to a flash memory and/or disk) every N^(th) iteration in a forward propagation phase 95 of the algorithm 72A. Each P_(S)(x,y,z,t) calculation step may include compressing the P_(S)(x,y,x,t) and then, writing of P_(S)(x,y,x,t) to memory. As shown in FIG. 7A, the forward pressure wave at every N^(th) timestep is represented as functions F( ) and are calculated in forward order (e.g., time t=N→time t=kN) in the model, as depicted by arrows 86, and these calculations are first saved to associated local memory (e.g., cache). Then, there is calculated reverse propagation, P_(R)(x,y,z,t) at every N^(th) timestep. That is, in a reverse propagation phase 96, the backward or reverse pressure wave represented as function R( ) is calculated in reverse order according to the time steps, e.g., by using the forward pressure wave data (obtained starting at time t=kN down to time t=N) stored at the local node memory. As the imaging condition requires matching at the same time, then all forward calculations of the imaging are obtained before the reverse wave calculations are made. Thus, during the calculation of the reverse pressure wave data, all the values for the forward propagation are obtained first. The calculations performed in the reverse propagation phase 96 include calculating reverse power pressure wave P_(R)(x,y,z,t) at every N timesteps according to the reverse time flow represented by arrows 87, which steps include reading the prior stored/loaded P_(S)(x,y,x,t) from memory, decompressing P(x,y,x,t) and calculating R( ) at that step. During these steps in reverse propagation phase 96 as depicted by arrows 88, there is further calculated the partial sum of the image, represented as function I( ) at each time step (in reverse order). For example, at step t=kN, the reverse propagation phase will include the calculating of the partial images I(kN) from the stored/loaded F(kN) and R(kN), I((k−1)N) values from stored/loaded F((k−1)N) and R((k−1)N) in reverse order, etc., until an image I(N) is computed. Then, at step 80, the final image I(x,y,z) 100 is computed by merging (combining) all the computed partial image values I(kN), I((k−1)N), . . . , I(N).

Particularly, in view of FIG. 6, temporary data for partial images created at each respective slave node 145 are stored in the respective local node memory. Alternately, combinations of memory storage modalities may be used including local memory (cache, main memory) and/or a flash memory storage device and/or scratch disk device. This data are communicated to the master node 130, which images may then be averaged and the final resulting image is obtained and saved for a single shot or metashot.

Continuing to FIG. 7B there is depicted a model according to a further embodiment for calculating the imaging condition. As in the imaging algorithm 72A (FIG. 7A), there is first loaded the Velocity model v(x,y,z); source and receiver data. Then, in the forward propagation phase 195 of the algorithm, P(x,y,z,t), is calculated every N timesteps. However, as different from the imaging algorithm of FIG. 7A, the forward propagation phase 195 is passed twice: 1) once as indicated at time steps 192 for saving boundary data instead of saving the snapshot of the whole volume in interest, exterior boundary values are saved and used to re-compute the interior value in the second pass; and, 2) once in “reverse” using the saved boundary data as indicated at time steps 194. That is, as shown in FIG. 7B, the forward pressure wave P_(S)(x,y,z,t) at a timestep is represented as functions F( ) and is calculated in forward order (e.g., time t=N→time t=kN) in the model, and these boundary data calculations at steps 192 are written to cache memory local to the Blue Gene® slave computing node 145 every N^(th) iteration thus avoiding the need for scratch disk as indicated by absence of disk storage units 150 as shown in FIG. 6.

As further shown in FIG. 7B during backward or reverse propagation phase 196 reverse pressure wave represented as function R( ) is calculated in reverse order in lock step with the “reverse” forward propagation pressure wave run obtained during time steps 194 (i.e., obtained starting at time t=kN down to time t=N). The calculations performed in the reverse propagation phase 196 include calculating P_(R)(x,y,z,t) at every N timesteps occurs according to the flow represented by arrows 177, which steps include reading the prior stored/loaded P_(S)(x,y,x,t) from local Blue Gene® node cache memory (RAM, or alternatively, RAM and flash memory, or RAM/flash and disk storage), decompressing P(x,y,x,t) and calculating R( ) at that step. During these steps in back propagation phase 196 as depicted by arrows 178, there is further calculated the partial sum of the image, represented as function I( ) at each time step (in reverse order). For example, at step t=kN, the reverse propagation phase will include the calculating of the partial images I(kN) from the stored F(kN) and R(kN), I((k−1)N) values from stored/loaded F((k−1)N) and R((k−1)N) in reverse order until I(N) is computed. Finally, at the last time step (in reverse, i.e., at time t=N in the example shown in FIG. 7B), the final image I(x,y,z) 200 is computed by merging (combining) all the computed partial image values I(kN), I((k−1)N), . . . , I(N).

Particularly, referring back to FIG. 6, the temporary data for partial images created and stored in cache memory (RAM, and/or the flash and disk memory storage arrangements described) at each respective compute node 145 are communicated to the master node 130, which images may then be averaged and the final resulting image 200 obtained and saved for a single shot.

As known FWI includes processing using iterative RTM processing as an inner loop including steps 405-437 that iterates over RTM. In one embodiment, RTM processing is iterated many times until the final RTM model converges. Thus, the image RTM generates is used in the iterative approach for refining the seismic model. That is, there is generally performed obtain RTM model and generate image, and that image is used to update seismic model, and the updated model is used for generating a further refined RTM model. And this FWI algorithm is repeated until some model convergence criteria are met.

FIG. 10 depicts a method 400 for FWI Seismic modeling performed on a massively parallel system (on the BGP supercomputer) according to one embodiment. As indicated at 402, there is first partitioned and loaded for storage the seismic trace data into node memory (e.g., RAM and/or flash memory at the node), and, at 404 there is initialized the FWI operating parameters, e.g., velocity model, density/porosity models, parameters directed to aspect of the velocity model in x, y, z, directions, (isotropy), etc. At 407 there is extracted and mapped to local storage memory at the node the model, source, and receiver (shot trace) data for the shot, or in additional embodiments, metashot (combined shot data). That is, the shot data could be combined shot data or single shot at a time—the combined shot or “metashot” as described herein, formed out of adding a subset of the shot data at like time steps of successive shots or sub-set of shots, or adding data from unique shots combined to form said metashot, using a variable weighting factor when combining shots into a metashot, or adding using combined shots as if they were all recorded at the same time, or adding by combining shots with a time lag, or forming a combination including a linear superposition of the recorded waves or a nonlinear superposition, etc. Then at 409 there is conducted forward modeling using the extracted/mapped model and source data at each node as described herein. The mapped data includes the partitioned velocity model domain representing a subsurface structure of the earth in said defined volume into a plurality of partitioned blocks where data representing measurement each wave produced by a shot of a sequence of plural shots are received at local storage devices and each partitioned domain block being assigned to one or more processing nodes of a distributed processing highly parallel computer device such as a Blue Gene/P (BGP) ultrascalable petaflop parallel supercomputer described below. Concurrently, the extracted trace data is received at the respective node for generating the residual data at 411. The residual data is the difference between the gather trace data and the data computed from the forward processing using the model in interest. Then, at 413, the backward propagated wave data is calculated using the residual data obtained at step 411. Continuing to 420, updating factors for tuning the model in interest are generated (e.g., using a gradient approach) and accumulated using the calculated forward wave propagation data computed at step 409 and the backward propagation data computed at step 413. These updating factors form a correction term which are used to discern whether the RTM model needs updating.

The process proceeds from 420 to step 435 where the determination is made as to whether any further shot data remains to be processed in which case new shot data is obtained at 440 and the process repeated by returning to 407, FIG. 10 for continued shot data processing. Otherwise, if at 435, it is determined that there are no more shots to process, then the process proceeds to 450 to determine if the seismic model is acceptable. If at 450 it is determined that the seismic model is still unacceptable, the process proceeds to 460 to update the seismic model and return to step 407 to begin a new iteration of processing using the updated factors.

Otherwise, at 450, if the RTM model is acceptable, the FWI process completes.

It is understood that, in an alternative embodiment, FIG. 10 is modified to orient the RTM imaging problem as an error minimization problem. That is, the difference between the received (measured) receiver (trace) data (e.g., for a shot) and the estimated receiver data generated as computing using the forward modeling, (forward wave propagation computations) may be used to update the model in an iterative fashion in a fashion similar to RTM processing.

As mentioned, the Blue Gene® system is a distributed-memory supercomputer. The aggregate memory of the total machine is distributed in the style of multi-computer. With each compute node 145 (FIG. 6) supporting up to 4 GB physical memory, a rack of the Blue Gene® system can have up to 4 TB aggregate memory.

The system, method and computer program product for use in the Blue Gene® system uses its aggregate memory as a high performance data fabric for handling intermediate data in Reverse Time Migration (RTM) seismic imaging process.

In an example implementation, the RTM seismic imaging process may be performed on two racks of a Blue Gene/P (alternately referred to herein as “BGP”) system such as described in Sosa, C and Knudson, B., 2009. IBM System Blue Gene Solution: Blue Gene/P Application Development, IBM Redbooks, http://www.redbooksibm.com/abstracts/sg247287.html.

Further details concerning the BGP system operation can be found in commonly-owned U.S. Pat. No. 7,761,687 entitled Ultrascalable Petaflop parallel supercomputer, the entire contents and disclosure of which is incorporated by reference as if fully set forth herein. For example, an implementation of a Blue Gene/P (BGP) supercomputer has 1024 nodes per rack, running at 0.85 GHz. Each node has 4 single-threaded cores, 4 GB of RAM per node (4 TB per rack) and an extremely high bandwidth, low-latency, nearest-neighbor 3D torus topology network in which each node is connected to each of its 6 nearest neighbor nodes by 850 MB/s of send+receive bandwidth (i.e., 5.1 GB/s per node and 5.22 TB/s of communication bandwidth per rack). Because of this massive bandwidth, BGP is suited for physical modeling involving extensive nearest-neighbor communication and synchronization. The nearest neighbor latency for 32 B data transfers is about 0.1 microseconds and is essentially amortized away for larger block transfers required by RTM. Each compute node core has a 32 KB L1 cache with a 32 B cacheline and a shared 8 MB L3 cache with a 128 B cacheline. Each node has two memory channels with an aggregate bandwidth of 13.6 GB/sec to main memory. BGP compute notes are connected via dedicated I/O nodes to a GPFS file system based on three DDN S2A9900 couplets attached to the BGP I/O nodes via 10 Gigabit Ethernet connections, providing ˜16 GB/s of disk I/O bandwidth per rack. Each node can operate in SMP mode as a unit, or as four “virtual” nodes. The Virtual Node (VN) model avoids the need to explicitly use multithreading at the node level and thereby eases programmability. Each core has a 2-way SIMD unit.

More particularly, FIG. 8 is a block diagram illustrating a single computing node ASIC 145 according to the principles of the invention. Each node preferably is based on the chip process that integrates all the functions of a computer into a single compute ASIC, enabling dramatic reduction of node size and power consumption. In a supercomputer, this can be further leveraged to increase node density thereby decreasing the overall cost/performance for the machine. As shown in FIG. 8, the ASIC of this design, which may function as both a compute node and an I/O node in the system, include four processing cores 11, each having a “double” floating point unit 14, that includes two coupled standard floating point units. This arrangement gives a peak performance of four floating point operations per processor core per clock cycle. The processor core is a PowerPC450 embedded core, e.g., available from International Business Machines, Inc. (IBM), although future versions of this core may be used as technology improves. The “Double” FPU unit increases the data bandwidth by increasing the datapath from 64 bits to 128 bits to allow for quadword Floating Point loads and stores (i.e., data moving). Additionally, this ASIC unit has been architected to allow two floating point multiply-add instructions to be dispatched and executed in one cycle. The dual floating point pipelines allow for architected (single instruction, multiple data) instructions for complex number arithmetic. As an example shown herein below, consider a code fragment which performs an operation A*B+C on three complex numbers, A, B and C. Assume that prior to the computation, the registers ar and ai contain the real and imaginary parts of A, and similarly, the pairs br and bi, and cr and ci hold the values of B and C. A compiler would automatically be able to generate the following code, requiring just two instructions, which places the result into a register pair dr and di.

ar * br + cr → tr; ar * bi + ci → ti first FMA SIMD instruction −ai * bi + tr →dr; ai * br + ti → di second SIMD instruction

The node further incorporates other functions into the ASIC. Besides the embedded processing core and floating point cores, the system includes embedded DRAM 15, an integrated external DDR2 memory controller, a Direct Memory Access (DMA) module 16, 10 Gb Ethernet interface and associated functionality 19 as well as all the network link cut-through routing buffers and routing control block that allow any two nodes to communicate with low latency. The compute node in one embodiment includes four embedded cores 11, such as the PPC450, each capable of being utilized for message handling and computation operations.

As further shown in FIG. 8, virtual cut-through torus routing is supported in hardware block 22, which is integrated into the ASIC allowing for the elimination of the network adapter. Preferably, a virtual channel routing network is supported with two (2) dynamic and two (2) deterministic channels.

The details of DMA feature of the torus network may be found in the co-pending U.S. Pat. Nos. 7,788,334, 7,886,084, 7,694,035, 7,802,025, and U.S. patent application Ser. Nos. 11/768,682, 11/768,813.

As implemented in the massively parallel supercomputer of the invention having multiple nodes 145 as shown in FIG. 6, the direct memory access (DMA) engine 16 permits certain hardware sub-systems within a computer system to access system memory for reading and/or writing that is independent of the central processing unit, or compute nodes comprising processor(s) in the case of parallel computer system. A DMA transfer comprises functions for copying a block of memory (data) from one device to another within a computer or computer system, e.g., from system RAM to or from a buffer on the DMA device w/o interrupting the processor operation. The CPU initiates the DMA transfer, but the DMA carries out the task. Further use of the DMA 16 engine is made by disk drive controllers, graphics cards, network cards, sound cards and like devices.

Computer systems that employ DMAs and DMA message passing can transfer data to and from system devices with much less CPU overhead than computer systems constructed to message and pass data without a DMA engine or channel. For example, the BlueGene/P massively parallel supercomputer (“BGP supercomputer”), includes a DMA engine integrated onto the same chip as the processors (CPUs), cache memory, memory controller and network logic.

One operation facilitated by use of the DMA engine in the processing node is the sharing of reception and injection byte counters among the network slave (compute) nodes (for both computation and I/O tasks or applications) and respective processor core elements in the interconnected as a network. Each compute node, or I/O node comprising the parallel computer system includes a plurality of processors, memory and a DMA engine, constructed from a single ASIC such that DMA resources, e.g., DMA reception and injection byte counters, are limited. As such, the system provides that the processors and the DMA can write and read the shared byte counters in such a way that more outstanding messages can be supported by the DMA engine, and therefore the parallel computer system.

The ASIC nodes 145 (FIG. 8) comprising the parallel computer system that are interconnected by multiple independent networks optimally maximize packet communications throughput the system with minimal latency. As mentioned herein, in one embodiment of the invention, the multiple networks include three high-speed networks for parallel algorithm message passing, including the Torus with direct memory access (DMA), collective network, and a Global Asynchronous network that provides global barrier and notification functions.

Furthermore, at least four modes of operation are supported: the virtual mode, SMP 1-core mode, SMP 4-core mode, and a dual mode. In the virtual node mode, each of the processing cores will perform its own MPI (message passing interface) task independently. Each core uses approximately one-quarter of the memory (L3 and DRAM) of the compute node, while coherence among the four MPI within the node and across the nodes is maintained by MPI. In the SMP (Symmetric Multi Processor) 1-core mode, one core performs a single MPI task, using the entire memory capacity of the node. In the SMP 4-core mode, one MPI task with 4 threads is running, using the whole node memory capacity. The fourth or dual mode is a hybrid case, wherein two SMP MPI tasks are running, with each SMP using 2 processor cores running a thread each. Finally, one can also support modes such as a 1, 3 split, and 1, or 2 or 3 cores idling. Thus a compute node can trade off amount of memory versus parallelism, a feature unique to this supercomputer, or parallel computer system.

Because of the torus's DMA feature, internode communications can overlap with computations running concurrently on the compute nodes. Also, complex forms of messaging protocols, particular arithmetic functions, often called “reduction functions”, are invoked on message data as it arrives. One compute node core, or processor, may be designated to perform these functions without distracting computations on other processor cores. Additionally, because of the computational power of the I/O processor, the application is able to define arbitrarily complex reduction functions, supporting new algorithmic development that overlaps computational power with communication activities. For particular classes of parallel algorithms, or parts of parallel calculations, this architecture may apply the power of some or all cores at a particular compute node to work in collaboration on communication activities.

Further details regarding implementation of Blue Gene/P high performance computer can be found in Sosa, C and Knudson, B., entitled IBM System Blue Gene Solution: Blue Gene/P Application Development, IBM Redbooks, http://www.redbooks.ibm.com/abstracts/sg247287.html, 2009, the entire contents and disclosure of which is incorporated by reference as if fully set forth herein.

As mentioned, the nodes in the Blue Gene® system are interconnected through multiple networks. Each compute node (slave) 145 has six connections to the torus network. The torus network connects the nearest neighbors into a three dimensional torus. The torus network can be used for general purpose, point-to-point messaging passing and multicast operations to a selected class of nodes.

Further to the system and method in the Blue Gene® system, use is further made of torus network as a high performance data communication mechanism for partitioning each shot gather among a subset of the Blue Gene® nodes and performing RTM seismic imaging in a collaboration fashion.

As described with respect to FIG. 9, the physical machine architecture is related to n-dimensional torus 50 which in the example embodiment, is a 3-dimensional nearest neighbor interconnect that is “wrapped” at the edges. All neighbor nodes 145 are equally distant, except for time-of-flight differences such as exist between different racks of ASICs. The nearest neighbors may be four times the processor speed (e.g., 3.4 Gb/s in each direction) in an example embodiment. Each node therefore supports 6 independent bi-directional nearest neighbor links with an aggregate bandwidth of 5.1 GB/s, for example. In one example embodiment, the system circuit cards are wired in sub-cubes while mid-planes, two per rack, are wired as sub-cubes.

The topology of network 50 of FIG. 9 is a three-dimensional torus constructed with bi-directional, point-to-point, serial links between routers embedded within the ASICs. Therefore, each compute node has six neighbor connections to the torus network, some of which may traverse relatively long cables. The torus network provides both adaptive and deterministic minimal-path routing, and is deadlock free. Throughput and latency are optimized through the use of virtual through (VCT) routing as described in the reference to P. Kermani and L. Kleinrock entitled “Virtual Cut-Through: A New Computer Communication Switching Technique, “Computer Networks, Vol. 3, pp. 267-286, 1979 incorporated herein by reference. Messages may be composed of multiple packets, which are the atomic units of routing. Therefore, adaptively-routed packets from the same message may arrive out of order. Packets are variable in size, ranging from 32 bytes to 256 bytes with a granularity of 32 bytes (i.e., one to eight 32-byte chunks per packet).

As mentioned, Virtual channels (VCs) are used to provide deadlock-free adaptive routing and increase throughput and the torus network in the supercomputer and may have four or more VCs in a configuration whereby two VCs employ adaptive routing, and two employ deterministic routing. One of the deterministic VCs is used as an “escape channel” for the adaptive sub-network in order to guarantee deadlock freedom, and the other is reserved for high-priority packets. Because it is expected that most traffic will be adaptively routed, two adaptive VCs are provided in order to reduce head-of-line blocking and allow for the use of simple FIFO buffers within the routers.

Flow control between routers is provided through the use of tokens because the latency across a cable allows multiple packets to be in flight simultaneously. There is sufficient VCT buffer space to maintain full link bandwidth in the absence of contention.

In the implementation of the RTM seismic imaging governed according to equation (3), there is used four 3D data objects: the past, present and future waves and the velocity model. In one embodiment, to increase the locality of the model, a ping-pong buffer pair may be used, whereby the current wave (data) is held in one buffer and the future and past waves (data) held in the second buffer [http://www.pcmag.com/encyclopedia_term/0,2542,t=ping-pong+buffer&i=49297,00.asp. In one embodiment, however, a first buffer (Buffer A) may be used to compute the values of a second buffer (Buffer B) and then use Buffer B values to compute the values in Buffer A—and iterate—in order to save memory storage space. This buffering is possible because once the future wave point is calculated, the past wave point is no longer needed and can be overwritten with the future value. This buffering reduces RTM's cache size requirements by 25% and thereby allows for processing larger models more efficiently.

An analysis of the various trade-offs made in this implementation of RTM is helpful in guiding the choice of operational parameters. This analysis shows that various system constraints prevents running at the theoretically optimal operational parameters. Consider a cubic velocity model of size N³ elements which is uniformly partitioned over K³ nodes such that each node is responsible for processing a sub-volume of size V=N³/K³. For any sub-volume, the time required to compute the stencil (e.g., stencil 20 shown in FIG. 3) over all the elements of the corresponding sub-volume is estimated and the time required to communicate boundary data to and from its nearest neighbors is estimated. A balanced implementation utilizes equal time for these tasks so as to efficiently utilize all the machine's resources.

The 2^(nd) order in time and 8^(th) order in space finite difference method used in Equation (3) to approximate wave propagation gives rise to ˜32 floating-point operations for each stencil calculation, if one pre-computes the spatial and temporal deltas into the stencil parameters. That is, the stencil/method instructions are coded into the assembly code at each processor; each processor having differences in what instructions are available and what assembly code sequences lead to the best performance. Depending on these details, the actual number of floating point operations will general vary. This pre-computation is possible here since the deltas are constant for RTM. Letting F be the peak number of FLOPS per node, then a total time to compute each sub-volume is bounded below by TCompute=32(N/K)³/F.

A critical aspect of domain-partitioned RTM is that current wave data from neighboring sub-domain boundaries is required for stencil calculations at each time step. That is, as mentioned, the stencil in one partition may require data from a neighboring partition—which necessitates the transfer of boundary data between compute nodes for each time step of the algorithm. Since this boundary data transfer grows with the amount of partitioning and with the size of the stencil used, it can easily become a performance bottleneck. To avoid communication bottlenecks, the partitioned RTM on a Blue Gene/P supercomputer is designed specifically for extremely efficient inter-node communication attributable to the Torus network and efficient inter-node communications bandwidth.

That is, for each pass of the stencil over a wave sub-volume (volume partition), the boundary regions need to be communicated between nearest neighbor nodes as illustrated by bi-directional arrows shown in FIG. 6A that depicts the nearest neighbor communications for calculations performed for stencil 220 for a sub-volume velocity model partition at a node 145. FIG. 6A shows as a result of RTM domain partitioning in the model depicted in FIG. 6, efficient neighboring node communication as the wave equation stencil uses data from neighboring nodes 145 a, 145 b, 145 c, 145 d in its calculations at a node. In the processing, the equation stencil uses data from neighboring nodes, e.g., using MPI message communication between nodes.

For example, throughout the partitioned model, in the calculation at partition 145 e, as shown in FIG. 6A. The boundary data shared between neighboring partitions would include data from each of neighboring nodes 145 a, 145 b, 145 c, 145 d, in order to perform the stencil calculations of stencil 220 i.e., when the stencil is at an edge of the partition. This data is sent efficiently via BlueGene.

Since the Blue Gene torus network allows nodes to send and receive data simultaneously, and since it has independent paths for each of the spatial (e.g., x-y-z-dimensions), it can be assumed that these nearest neighbor data transfers all happen at approximately the same time for each node. Further, since the algorithm sends the same amount of data between all nearest-neighbor nodes, the time of a single boundary transfer characterizes the communication behavior of the node. In one embodiment, the amount of data transferred for each finite difference time step is 4 bytes per element, 4 elements per stencil calculation per-dimension and one stencil calculation for each element on a face of the sub-volume.

Dividing this data by the peak torus send bandwidth, D, between each node gives a total time of TData=16(N/K)²/D. This analysis shows that TCompute/TData=2ND/KF. For an ideal balanced system, this ratio is a value one (1), and N and K may be appropriately chosen.

Constraints exist that prevent choosing N and K arbitrarily. In particular, in one embodiment, there is stored all of the RTM models (e.g., velocity and two time steps of wave volume) in cache because complete cache locality gives a dramatic performance advantage. For an example RTM implementation, there is fixed 3 sub-volumes of size V in cache. Thus V<8/3 Mbytes for the example BGP implementation described herein. Since V=N³/K³, it is seen that N/K<89 which implies N/K<56 per core. For a rack, this means a velocity model of size 880³ fits in the cache implementation in BGP.

In a further embodiment, there may be considered several additional constraints on the block dimensions. The L1 cache line length imposes a preferred granularity in the stride-one (z) dimension of 8 floats (32 B). The cache is used more effectively if the number of cache lines in the z dimension is not a factor or multiple of the number of sets in the set-associative cache (e.g., 16 for BGP), since otherwise memory accesses will be concentrated in some portions of the cache while other portions remain unused.

In a further embodiment, cache tiling is implemented to enable each dimension of the block be a multiple of the corresponding tile dimension. For example, improved performance may be achieved with a block size of 54×54×56 rather than 55³.

Choices of this nature trade kernel performance and MPI performance since asymmetry to favor stride-one dimension efficiency leads to higher communication requirements and help balance implementation. Additionally, the RTM imaging implementation saves snapshots data to main memory to avoid disk I/O bottlenecks. This choice imposes another constraint on the data: the model in cache is small enough to allow a sufficient number of snapshots to be saved.

Typically, production RTM runs can be on the order of five to ten thousand forward iterations, however due to disk storage and bandwidth constraints, practitioners typically subsample the data in time, saving only a fraction of the wave fields according to a pre-specified “snapshot” frequency.

Common snapshot frequencies range from 3-10 iterations per snapshot, depending on the RTM imaging requirements. For Blue Gene®, this implies up to about 1500 snapshots (=memory size/one-third the cache size), which imposes a snapshot frequency range of 3-7 iterations per snapshot. More snapshots can be saved (e.g., for higher image quality or more time iterations) however, by reducing the size of V and run on more nodes; or reduce the size and/or number of snapshots (e.g., by sub-sampling and/or compressing snapshots); or save some of the snapshots to disk. One example implementation includes all of these options.

Note that this analysis also shows that for practical values of N and K, TData is much larger that the MPI latency of both Blue Gene systems. So there is no MPI latency bound. Rather domain partitioning allows partitioning the domain over different numbers of computing nodes and thus takes advantage of the cache structure of the platform. When the partitioned subvolume can fit in processor cache, it allows processing to proceed at the speed of the cache memory bandwidth instead of main memory bandwidth.

As will be appreciated by one skilled in the art; aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a circuit, module or system. Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with a system, apparatus, or device running an instruction. The containment (or storage) of the program may be non-transitory.

A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with a system, apparatus, or device running an instruction.

Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may run entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

Aspects of the present invention are described below with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which run via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.

The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which run on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more operable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be run substantially concurrently, or the blocks may sometimes be run in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

While there has been shown and described what is considered to be preferred embodiments of the invention, it will, of course, be understood that various modifications and changes in form or detail could readily be made without departing from the spirit of the invention. It is therefore intended that the scope of the invention not be limited to the exact forms described and illustrated, but should be construed to cover all modifications that may fall within the scope of the appended claims. 

Having thus described our invention, what we claim as new, and desire to secure by Letters Patent is:
 1. A computer-implemented method for creating a Reverse Time Migration seismic model of sub-surface formations in a defined 2D or 3D volume of a geological structure using a Full Waveform Inversion computation, said method comprising: partitioning a velocity model domain representing a subsurface structure of the earth in said defined volume into a plurality of blocks, each block having an associated processing task for processing wave data associated with a shot; assigning each partitioned domain block to processing nodes of a distributed processing parallel computer device having a plurality of processing nodes interconnected through one or more communication networks; receiving, at a local storage device associated with a respective processing node, a trace data representing measurement of each wave produced by a shot of a sequence of plural shots, each local storage device comprising a local cache or flash memory storage device coupled with a processor device at the processing node; computing, in parallel, using said associated processing tasks operating on said received trace data associated with a shot at each said processing node, contributions of forward wave propagation data and reverse wave propagation data at that node, said reverse wave propagation data computed using a residual data from forward wave propagation data computing, wherein said forward or reverse wave propagation data contributions are computed at the processing node and stored at the local cache or flash memory storage device at the processing node; and using said computed forward wave propagation data and reverse wave propagation data contributions stored at the local cache or flash memory storage device at the processing node to compute a correction term from which the seismic model is updated, the seismic model updating including, for each shot, iteratively performing: computing, in parallel, said contributions of forward wave propagation data; obtaining said residual data representing a difference between said received trace data and data from said forward wave propagation computations; determining an accuracy of said seismic model based on said obtained residual data; and updating said seismic model based on said determining, the updated seismic model minimizing an error in modeling the sub-surface formations.
 2. The computer-implemented method as in claim 1, further comprising: combining, at a respective partitioned node, receiver data of two or more shots to form a metashot, said associated processing tasks operating on formed metadata at each said processing node.
 3. The computer-implemented method as claimed in claim 2, wherein said processing at each node comprises: calculating in a forward path current forward wave propagation data from a wavelet representing a model of said source wave at predetermined time steps for a full forward path and storing boundary values; and, computing reverse wave propagation data representing reverse propagating waves in said volume using said residual data, while re-calculating forward path data representing forward propagating wave in reverse time order using previously saved boundary value data; computing, using said re-calculated forward wave propagation data and reverse wave propagation data, a correction term at each node; and, summing said computed correction terms from each node to create the correction term from which the seismic model is updated.
 4. The computer-implemented method as claimed in claim 3, wherein the re-calculated forward path data represents forward propagating wave in reverse time order and is stored incrementally in said local memory storage device.
 5. The computer-implemented method as claimed in claim 1, configuring each said node for pipelined processing wherein said forward or reverse wave propagation components are computed/stored at the processing node for current shot data while new data for the next shot is loaded into said local memory storage device at each node.
 6. The computer-implemented method as claimed in claim 5, wherein, for each shot, said iteratively performing including: extracting from said local memory storage devices, source data and receiver data representing shot data at one or more processing nodes.
 7. The computer-implemented method as claimed in claim 5, wherein said processing at each node comprises: calculating current forward wave propagation data from a wavelet representing a model of said a source at predetermined time steps; storing calculation results of said forward wave propagation data at one or more time instances at said local memory storage device associated with said node; calculating said reverse wave propagation data representing reverse propagating waves in said volume using said residual data; and, computing, using said forward wave propagation data and reverse wave propagation data, a partial image at each node.
 8. A computer-implemented method for creating a Reverse Time Migration seismic model of sub-surface formations in a defined 2D or 3D volume of a geological structure using a Full Waveform Inversion computation, said method comprising: partitioning a velocity model domain representing a subsurface structure of the earth in said defined volume into a plurality of blocks, each block having an associated processing task for processing wave data associated with a shot; assigning each partitioned domain block to processing nodes of a distributed processing parallel computer device having a plurality of processing nodes interconnected through one or more communication networks; receiving, at a local storage device associated with a respective processing node, a trace data representing measurement of each wave produced by a shot of a sequence of plural shots; each local storage device comprising a local cache or flash memory storage device coupled with a processor device at the processing node; combining, at a respective partitioned node, receiver data of two or more shots to form a metashot, said associated processing tasks operating on formed metadata at each said processing node; computing, in parallel, using said associated processing tasks operating on said received trace data associated with a metashot at each said processing node, contributions of forward wave propagation data and reverse wave propagation data at that node, said reverse wave propagation data computed using a residual data from forward wave propagation data computing, wherein said forward or reverse wave propagation data contributions are computed at the processing node and stored at the local cache or flash memory storage device at the processing node; and using said computed forward wave propagation data and reverse wave propagation data contributions stored at the local cache or flash memory storage device at the processing node to compute a correction term from which the seismic model is updated, the seismic model updating including, for each metashot, iteratively performing: computing, in parallel, said contributions of forward wave propagation data; obtaining said residual data representing a difference between said received trace data and data from said forward wave propagation computations; determining an accuracy of said seismic model based on said obtained residual data; and updating said seismic model based on said determining, the updated seismic model minimizing an error in modeling the sub-surface formations.
 9. The computer-implemented method as claimed in claim 8, further comprising: configuring each said node for pipelined processing wherein said forward or reverse wave propagation components are computed/stored at the processing node for current metashot data while new data for the next metashot is loaded into said local memory storage device at each node.
 10. The computer-implemented method as claimed in claim 9, wherein said computing at each node comprises: calculating in a forward path current forward wave propagation data from a wavelet representing a model of said source wave at predetermined time steps for a full forward path and storing boundary values; and, computing reverse wave propagation data representing reverse propagating waves in said volume using said residual data, while re-calculating forward path data representing forward propagating wave in reverse time order using previously saved boundary value data; computing, using said re-calculated forward wave propagation data and reverse wave propagation data, a correction term at each node; and, summing said computed correction terms from each node to create the correction term from which the seismic model is updated.
 11. The computer-implemented method as claimed in claim 10, wherein the re-calculated forward path data represents forward propagating wave in reverse time order for is stored incrementally in said local memory storage device.
 12. The computer-implemented method as claimed in claim 8, wherein, for each metashot, said iteratively performing including: extracting from local memory storage devices, source data and receiver data representing metashot data at one or more processing nodes.
 13. The computer-implemented method as claimed in claim 12, wherein combined metashot data is incrementally loaded into said local memory storage device at each node.
 14. The computer-implemented method as claimed in claim 8, wherein said computing at each node comprises: calculating current forward wave propagation data from a wavelet representing a model of said source at predetermined time steps; storing calculation results of said forward wave propagation data at one or more time instances at said local memory storage device associated with said node; calculating said reverse wave propagation data representing reverse propagating waves in said volume using said residual data; and, computing, using said forward wave propagation data and reverse wave propagation data, a partial image at each node.
 15. The computer-implemented method as claimed in claim 8, wherein said combining comprises: adding a subset of the shot data at corresponding time steps of shots or sub-set of shots at corresponding spatial points of the volume, said subset of shot data selected randomly or according to one or more rules.
 16. The computer-implemented method as claimed in claim 8, wherein said combining receiver data of two or more shots includes using a variable weighting factor when combining shots into a metashot.
 17. The computer-implemented method as claimed in claim 8, wherein a combination of receiver data includes a linear or a nonlinear superposition of the recorded waves.
 18. A system for creating a Reverse Time Migration seismic model of sub-surface formations in a defined volume of a geological structure using a Full Waveform Inversion computation, said system comprising: an array of receiver devices at or within said defined volume for recording trace data representing measurements of each wave produced by a shot of a sequence of plural shots; a distributed processing parallel computer device having a plurality of processing nodes interconnected through one or more networks, each node having a respective processor device and a local memory storage device associated with the respective processor device, each local storage device comprising a local cache or flash memory storage device coupled with a processor device at the processing node, wherein one or more said processing nodes is assigned a processing block representing one partition of a partitioned velocity model domain representing geophysical wavefield propagation characteristics of a sub-surface structure of the earth in said defined volume, each processing block having an associated processing task for processing wave data associated with a shot; wherein a processor device at each node is configured to perform, in parallel, a method comprising: combining, at a respective partitioned node, recorded trace data of two or more shots to form a metashot, said associated processing tasks operating on said formed metashot at each said processing node; computing, in parallel, using said associated processing tasks operating on said recorded trace data associated with a metashot at each said processing node, contributions of forward wave propagation data and reverse wave propagation data at that node, said reverse wave propagation data computed using a residual data from forward wave propagation data computing, wherein said forward or reverse wave propagation data contributions are computed at the processing node and stored at the local cache or flash memory storage device at the processing node; and using said computed forward wave propagation data and reverse wave propagation data contributions stored at the local cache or flash memory storage device at the processing node to compute a correction term from which the seismic model is updated, the seismic model updating including, for each metashot, iteratively performing: computing, in parallel, said contributions of forward wave propagation data; obtaining said residual data representing a difference between said received trace data and data from said forward wave propagation computations; determining an accuracy of said seismic model based on said obtained residual data; and updating said seismic model based on said determining, the updated seismic model minimizing an error in modeling the sub-surface formations.
 19. The system as claimed in claim 18, wherein each said node is further configured to perform pipelined processing wherein said forward or reverse wave propagation components are computed/stored at the processing node for current metashot data while new data for the next metashot is loaded into said local memory storage device at each node.
 20. The system as claimed in claim 19, wherein said processor device at each node is configured to perform: calculating current forward wave propagation data from a wavelet representing a model of said source at predetermined time steps; storing calculation results of said forward wave propagation data at one or more time instances at said local memory storage device associated with said node; calculating said reverse wave propagation data representing reverse propagating waves in said volume using said residual data; and, computing, using said forward wave propagation data and reverse wave propagation data, a partial image at each node.
 21. The system as claimed in claim 20, wherein said processor device at each node is configured to perform: calculating in a forward path current forward wave propagation data from a wavelet representing a model of said source wave at predetermined time steps for a full forward path and storing boundary values; and, computing reverse wave propagation data representing reverse propagating waves in said volume using said residual data, while re-calculating forward path data representing forward propagating wave in reverse time order using previously saved boundary value data; computing, using said re-calculated forward wave propagation data and reverse wave propagation data, a correction term at each node; and, summing said correction terms from each node to create the correction term from which the seismic model is updated.
 22. The system as claimed in claim 18, wherein, for each metashot, at each said iteration, said processor device at each node is configured to perform, in parallel, a method comprising: extracting from said local memory storage devices, source data and receiver data representing metashot data at one or more processing nodes.
 23. The system as claimed in claim 18, wherein one of said one or more networks interconnecting said nodes includes a multi-dimensional torus or mesh network.
 24. The system as claimed in claim 18, wherein said local memory storage device for the data used to calculated the waves at a time step is a cache memory local to a processor at said compute node, a partitioned domain block fitting within said processor cache of a node to allow processing to proceed at an operating speed of a cache memory bandwidth. 